Question

Solve:
3x - 2y + z = 2
2x + 3y - z = 5
x + y + z = 6

• A. x = 1, y = 2, z = 3
• B. x = 2, y = 1, z = 3
• C. x = 3, y = 1, z = 2
• D. x = 2, y = 3, z = 1

Answer 1

The correct option is A x = 1, y = 2, z = 3

3x - 2y + z = 2 .....(1)
2x + 3y - z = 5.....(2)
x + y + z = 6 .....(3)

$eqn\left(1\right)+eqn\left(2\right)3x-2y+z=22x+3y-z=5$
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$5x+y=7.............\left(4\right)$

$eqn\left(2\right)+eqn\left(3\right)2x+3y-z=5x+y+z=6$
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$3x+4y=11.............\left(5\right)$

$eqn\left(4\right)\times 4-eqn\left(5\right)20x+4y=28-3x-4y=-11$
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$17x=17[x=1].............\left(6\right)$

Substituting eqn(6) in eqn(4), we get,
$5\left(1\right)+y=7[y=2]...........\left(7\right)$

Substituting eqn(6) and eqn (7) in eqn(3), we get,
$1+2+z=6[z=3]...........\left(8\right)$

Ans:
[x = 1]
[y = 2]
[z = 3]

Verification:

Substituting the values of x,y and z in eqn(2), we get,

$LHS=2\left(1\right)+3\left(2\right)-3=2+6-3=5=RHS$